scholarly journals Computing multi-mode shock-induced compressible turbulent mixing at late times

2015 ◽  
Vol 779 ◽  
pp. 411-431 ◽  
Author(s):  
T. Oggian ◽  
D. Drikakis ◽  
D. L. Youngs ◽  
R. J. R. Williams
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Suitable Model ◽  
Late Time ◽  
Flow Equations ◽  
Multi Mode

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

Numerical Simulations of Turbulent Mixing and Autoignition of Hydrogen Fuel at Reheat Combustor Operating Conditions

2011 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Berthold Noll ◽  
Peter Griebel ◽  
Manfred Aigner ◽  
Khawar Syed
Keyword(s):  
Natural Gas ◽  
Numerical Simulations ◽  
Flue Gas ◽  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Numerical Study ◽  
Operating Conditions ◽  
Fuel Blend ◽  
Flow Configuration ◽  
Modeling Methods

Turbulent mixing and autoignition of H2-rich fuels at relevant reheat combustor operating conditions are investigated in the present numerical study. The flow configuration under consideration is a fuel jet perpendicularly injected into a crossflow of hot flue gas (T > 1000K, p = 15bar). Based on the results of the experimental study for the same flow configuration and operating conditions two different fuel blends are chosen for the numerical simulations. The first fuel blend is a H2/natural gas/N2 mixture at which no autoignition events were observed in the experiments. The second fuel blend is a H2/N2 mixture at which autoignition in the mixing section occurred. First, the non-reacting flow simulations are performed for the H2/natural gas/N2 mixture in order to compare the accuracy of different turbulence modeling methods. Here the steady-state Reynolds-averaged Navier-Stokes (RANS) as well as the unsteady scale-adaptive simulation (SAS) turbulence modeling methods are applied. The velocity fields obtained in both simulations are directly validated against experimental data. The SAS method shows better agreement with the experimental results. In the second part of the present work the autoignition of the H2/N2 mixture is numerically studied using the 9-species 21-steps reaction mechanism of O’Conaire et al. [1]. As in the reference experiments, autoignition can be observed in the simulations. Influences of the turbulence modeling as well as of the hot flue gas temperature are investigated. The onset and the propagation of the ignition kernels are studied based on the SAS modeling results. The obtained numerical results are discussed and compared with data from experimental autoignition studies.

scholarly journals The effect of core size on the speed of compressible hollow vortex streets

2017 ◽  
Vol 836 ◽  
pp. 797-827 ◽  
Author(s):  
Darren G. Crowdy ◽  
Vikas S. Krishnamurthy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Vortex Core ◽  
Perturbation Expansion ◽  
Core Size ◽  
Flow Equations ◽  
Stable Case ◽  
First Order ◽  
Aspect Ratios ◽  
Vortex Streets

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Mach-number perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai–Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky–Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down.

scholarly journals A numerical study of a variable-density low-speed turbulent mixing layer

2017 ◽  
Vol 830 ◽  
pp. 569-601 ◽  
Author(s):  
Antonio Almagro ◽  
Manuel García-Villalba ◽  
Oscar Flores
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Incompressible Flows ◽  
Numerical Study ◽  
Density Ratio ◽  
Mixing Layer ◽  
Variable Density ◽  
The Self ◽  
Low Speed ◽  
Self Similar

Direct numerical simulations of a temporally developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier–Stokes equations in the low-Mach-number approximation are solved using a novel algorithm based on an extended version of the velocity–vorticity formulation used by Kim et al. (J. Fluid Mech., vol 177, 1987, 133–166) for incompressible flows. Four cases with density ratios $s=1,2,4$ and 8 are considered. The simulations are run with a Prandtl number of 0.7, and achieve a $Re_{\unicode[STIX]{x1D706}}$ up to 150 during the self-similar evolution of the mixing layer. It is found that the growth rate of the mixing layer decreases with increasing density ratio, in agreement with theoretical models of this phenomenon. Comparison with high-speed data shows that the reduction of the growth rates with increasing density ratio has a weak dependence with the Mach number. In addition, the shifting of the mixing layer to the low-density stream has been characterized by analysing one-point statistics within the self-similar interval. This shifting has been quantified, and related to the growth rate of the mixing layer under the assumption that the shape of the mean velocity and density profiles do not change with the density ratio. This leads to a predictive model for the reduction of the growth rate of the momentum thickness, which agrees reasonably well with the available data. Finally, the effect of the density ratio on the turbulent structure has been analysed using flow visualizations and spectra. It is found that with increasing density ratio the longest scales in the high-density side are gradually inhibited. A gradual reduction of the energy in small scales with increasing density ratio is also observed.

scholarly journals A numerical study of a turbulent mixing layer and its generated noise

2013 ◽  
Vol 56 (6) ◽  
pp. 1157-1164 ◽  
Author(s):  
Dong Li ◽  
Li Guo ◽  
Xing Zhang ◽  
GuoWei He
Keyword(s):  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Turbulent Mixing Layer

scholarly journals Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics

2014 ◽  
Vol 748 ◽  
pp. 113-142 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Spherical Surface ◽  
Density Ratio ◽  
Mixing Layer ◽  
Inertial Subrange ◽  
Planar Geometry ◽  
Late Time ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Decaying Turbulence

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

Numerical Simulations of Turbulent Mixing and Autoignition of Hydrogen Fuel at Reheat Combustor Operating Conditions

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Elizaveta M. Ivanova ◽  
Berthold E. Noll ◽  
Peter Griebel ◽  
Manfred Aigner ◽  
Khawar Syed
Keyword(s):  
Natural Gas ◽  
Numerical Simulations ◽  
Flue Gas ◽  
Turbulent Mixing ◽  
Turbulence Modeling ◽  
Numerical Study ◽  
Operating Conditions ◽  
Fuel Blend ◽  
Flow Configuration ◽  
Modeling Methods

Turbulent mixing and autoignition of H2-rich fuels at relevant reheat combustor operating conditions are investigated in the present numerical study. The flow configuration under consideration is a fuel jet perpendicularly injected into a crossflow of hot flue gas (T>1000K,p=15 bar). Based on the results of the experimental study for the same flow configuration and operating conditions, two different fuel blends are chosen for the numerical simulations. The first fuel blend is a H2/natural gas/N2 mixture at which no autoignition events were observed in the experiments. The second fuel blend is a H2/N2 mixture at which autoignition in the mixing section occurred. First, the non-reacting flow simulations are performed for the H2/natural gas/N2 mixture in order to compare the accuracy of different turbulence modeling methods. Here, the steady-state Reynolds-averaged Navier- Stokes (RANS) as well as the unsteady scale-adaptive simulation (SAS) turbulence modeling methods are applied. The velocity fields obtained in both simulations are directly validated against experimental data. The SAS method shows better agreement with the experimental results. In the second part of the present work, the autoignition of the H2/N2 mixture is numerically studied using the 9-species 21-steps reaction mechanism of O’Conaire et al. (Int. J. Chem. Kinet., 36(11), 2004). As in the reference experiments, autoignition can be observed in the simulations. Influences of the turbulence modeling as well as of the hot flue gas temperature are investigated. The onset and the propagation of the ignition kernels are studied based on the SAS modeling results. The obtained numerical results are discussed and compared with data from experimental autoignition studies.

Turbulent Hierarchic Structure and Scalar Mixing in a Supersonic Mixing Layer at High Convective Mach Numbers

2007 ◽  
Author(s):  
Hiroshi Maekawa ◽  
Daisuke Watanabe
Keyword(s):  
Mach Number ◽  
Shear Layer ◽  
Turbulent Mixing ◽  
Mixing Layer ◽  
Structure Evolution ◽  
Turbulent Shear ◽  
Scalar Mixing ◽  
Turbulent Structures ◽  
Turbulent Mixing Layer ◽  
Hierarchic Structure

Turbulent structures in a supersonic plane mixing layer at the convective Mach number of Mc=1.2 are studied using spatially developing DNS. High-resolution compact upwind-biased schemes developed by Deng & Maekawa (1996)[1] are employed for spatial derivatives. The numerical results indicate that the turbulent structures are generated after transition in the mixing layer, which are similar to the plane jet turbulent shear layer. The mixing layer Reynolds number based on the vorticity thickness reaches 6500. Unlike low Mach number mixing layers with a roller-like structure, hierarchic structures with hairpin packet-like structure and its cluster vortices are observed in the turbulent mixing layer. The effect of the turbulent hierarchic structure on scalar mixing is investigated using the DNS database. The visualized scalar field associated with vortical structure evolution of the turbulent mixing layer shows that the intermittent hairpin packet-like structure and its cluster govern a large-scale scalar mixing in the shear layer. The turbulent fine structure of pair vortices also plays an important role for scalar mixing. Furthermore, dilatational fields of the mixing layer show intense areoacoustic phenomena associated with the turbulent structure evolution.

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